{
  "id": "2406.18076",
  "version": "v1",
  "published": "2024-06-26T05:16:19.000Z",
  "updated": "2024-06-26T05:16:19.000Z",
  "title": "Continuum modeling for opinion formation on a network",
  "authors": [
    "Gianluca Favre",
    "Gaspard Jankowiak",
    "Sara Merino-Aceituno",
    "Lara Trussardi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider Abelson's model for opinion dynamics, where individuals interact if they are connected via a fixed network. Our aim is to develop a continuous description for these dynamics that captures well the global dynamics when the number of individuals grows to infinity. We aim at having a simple continuum description on which computations and comparison with the discrete dynamics are feasible. The difficulty lies in the network of connections being described through the labeling of the individuals: this makes the system not amenable to standard mean-field limits. We overcome this difficulty by introducing an evolving label-free network description. We compare the discrete model considered, and the continuum model proposed in the case of consensus dynamics, and carry out simulations for a system with three communities. Moreover, we propose extensions of the model to incorporate phenomena like creation and destruction of connections (dynamical networks), noise, and directional networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-26T05:16:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuum model",
      "opinion formation",
      "evolving label-free network description",
      "simple continuum description",
      "standard mean-field limits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}